# Definition:Absolute Value of Mapping/Real-Valued Function

## Definition

Let $S$ be a set.

Let $f: S \to \R$ be a real-valued function.

Then the absolute value of $f$, denoted $\size f: S \to \R$, is defined as:

$\forall s \in S: \map {\size f} s := \size {\map f s}$

where $\size {\map f s}$ denotes the absolute value function on $\R$.

Absolute value thence is an instance of a pointwise operation on real-valued functions.